1. Field of the Invention
The invention is directed to a method and an arrangement for displaying residual errors of a function which is fitted to a set of points.
2. Description of Related Art
A set of points comprises a plurality of discrete data points. At least two coordinates of a correspondingly multi-dimensional number space and a one-dimensional or multi-dimensional value are assigned to each of these points. The points can directly represent measurement data or can be derived indirectly from measurement data. A fitted function is an implicitly or explicitly defined assignment rule. It may or may not be constant and can be defined continuously or only at discrete points. Fitting to a set of points can be carried out, for example, by varying one or more function parameters within the framework of curve fitting or by other function variations.
Various algorithms are known in the art for fitting a predefinable or predefined function to a set of points by means of curve fitting. An example is the method of least squares deviation. Usually, the residual errors (residuals) of the fitted function are used for detailed assessment of the usefulness of a fit. With the help of these residuals, local deviations of the fitted function are easy to detect. To this end, the residual errors are usually depicted on a graph.
Methods for displaying residual errors of a fitted function are already known from the prior art. For example, Kolin et al. (Biophysical Journal, Vol. 90 (2006), 628-639, 638) show graphs with discrete data points and one-dimensional functions fitted to the data points. A second graph with the associated residuals is shown below every function graph, the graphs being oriented to one another along a coordinate axis.
Digman et al. (Biophysical Journal-Biophysical Letters BioFAST, 105.061788, L01-103, L03; Biophysical Journal, Vol. 89 (2005), 1317-1327, 1321) propose displaying two-dimensional fitted functions in perspective in a pseudo-3D rendering for raster image correlation spectroscopy. The associated residuals are displayed in a second graph, likewise in a perspective pseudo-3D rendering, above the function graph. The two graphs are oriented to one another along two coordinate axes. The data points are not shown in the graph of the fitted function because they cannot be interpreted in the perspective rendering. A color representation of the two graphs depending on the respective vertical coordinate is intended to increase the legibility of the perspective representation.
These known forms of data display have the disadvantage that an observer has difficulty distinguishing the quality of the fit of the function to the data points. With one-dimensional fits and two-dimensional fits, the observer must view two graphs simultaneously in order to obtain information about the quality of the fit. With a two-dimensional fit, the visual assignment of the residual errors to the fitted function is particularly difficult because of the perspective and is therefore inaccurate.